Annales Academić Scientiarum Fennicć
Mathematica
Volumen 32, 2007, 289-300

MARTIN BOUNDARY POINTS OF CONES GENERATED BY SPHERICAL JOHN REGIONS

Kentaro Hirata

Hokkaido University, Department of Mathematics
Sapporo 060-0810, Japan; hirata 'at' math.sci.hokudai.ac.jp

Abstract. We study Martin boundary points of cones generated by spherical John regions. In particular, we show that such a cone has a unique (minimal) Martin boundary point at the vertex, and also at infinity. We also study a relation between ordinary thinness and minimal thinness, and the boundary behavior of positive superharmonic functions.

2000 Mathematics Subject Classification: Primary 31C35; Secondary 31B05, 31B25.

Key words: Martin boundary points, cone, quasi-hyperbolic metric, John domain, thinness, minimal thinness, boundary behavior.

Reference to this article: K. Hirata: Martin boundary points of cones generated by spherical John regions. Ann. Acad. Sci. Fenn. Math. 32 (2007), 289-300.

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